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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12 (2019) pp. 2861-2872
© Research India Publications. http://www.ripublication.com
2861
Preview of Monomer Molar Equivalency in Polyurethane System: A model
study
Ankit Sharma1, Sushil K Sharma2 and Ashu Rani3
1,2,3 Department of Pure & Applied Chemistry, University of Kota,
Kota, Rajasthan-324 005, India.
Abstract
Polyurethane (PU) the organic polymers having monomers as
polyols and polyisocyanates, are joined by carbamate
(urethane) links. To understand the theoretical preview of PU-
Polymerization the concept of monomer mole ratio
equivalency have been used in the present research work,
monomer units taken are : chain extenders(CE) PEG-600
(polyethylene glycol) , cross linkagers (CLA)homogenous
mixture of 1,4-butanediol(BD) and 1,1,1-trimethylol propane
(TMP) , curing agents(CRA) 2,4-toluene diisocyanates. For
evaluating the extent of polymerization, NCO/OH (IR= index
ratio) have been evaluated by using mole concept and is
compared by using experimentally verified proposed models
[7nTDI -0.1]/2nCE+13nCLA while other models viz. 2nCE X 10 21 , 13nBD X 10 21, 13nTP X 10 21, for determining the number
of OH functionalities, for CE, BD, TMP respectively. While
for number of NCO functionalities of curing agent TDI , by
[7nTD-0.1] X 10 21, the extent of polymerization has been
studied through SEM images of PUC. The models for this PU
system is time effective , for evaluating the weight of CRA, a
model nTDI = [2nCE+13nCLA+0.1]/7is proposed with least
variability , the research work also envisages on the extent of
polymerization independency on the ratio of binary
components of CLA but depends on the weight of CLA taken
in the mixture, evaluated by the proposed model ∑ OH𝑇𝑀𝑃n +
∑ OH𝐵𝐷n = [W]CLA mix X 13 X 10 21 . Total OH
functionalities given by CLA & CE by proposed model is
given by 2nCE+13nCLA +0.1.Effect of w/w ratio variation of
binary components TMP and BD of CLA on the mechanical
properties of composite has been studied by evaluating
Tensile strength(TS) Young Modulus(YM) by Universal
testing machine(UTM) and hardness was evaluated by
durometer.
IR values less than unity incomplete polymerization, while for
IR values unity effective/complete polymerization was
noticed.
Keywords: chain extenders, cross linking agents, curing
agents, index ratio.
INTRODUCTION
Polyurethanes (PU)[1,2,15] are polymers made of organic
units joined by carbamates[29,32] (urethane) links , and are
formed when polyols (chain extenders: CE) [3,4,28]
containing two or more hydroxyl groups per molecule reacts
with molecules having two or more isocyanate group called as
the curing agent(CRA). The reaction between CRA [7, 18]
and CE is exothermic in nature; mixture becomes viscous and
eventually forms solid mass.
Ph
N
C
O
XHO OHPh
N
C
O
XHO OH
N
C
O
XHO OH
Ph
N
C
OH
XO OH
Ph
HN
C
O
XO OH
Ph
HNN C O
H
C
O
OCH2O
O O
C
NHH
O
O
C
NH
O
HN C O
O
H2C CH2N
H
C
O
O
C
NHH
O
C
NH
O
O
Mechanism of PU synthesis
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12 (2019) pp. 2861-2872
© Research India Publications. http://www.ripublication.com
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The properties of polyurethane [24, 25, 26, 30] is decided by
the nature of polyols and isocyantes being used, like soft and
elastic PU are formed by using polyols which render long
flexible segments while rigid PU having three dimensional
structure with high molecular weight can be synthesized by
using cross linking agents (CLA) [5, 6,16, 17,23],
CLA[19,27,31] are monomers having two or more
functionalities with two, three or four crosslinking sites.
Amount of CRA required for complete linkage of NCO
functionalities with OH not only depends on the concentration
of CE [20,21,22] solely, but also on the concentration of the
additives added to the mixture having OH functionalities too.
The general formula for evaluating the concentration of the
curing agent for PU synthesis is Wcur = IR[EWcur][Ʃ Wn/EWn].
where Wcur is weight of curing agent, EWcur is NCO Eq. Wt of
curing agent, Wn is weight of each liquid components, EWn is
OH Eq.Wt for each liquid, IR is index ratio for NCO to
OH[8,9,10,11,12], Eq.Wt for hydroxyl compound is
56100/hydroxyl number, and for isocyantes Eq.Wt. is
4200/%NCO. The formula incorporates NCO and OH values,
whose determination is through volumetrically or
potentiometrically. The same evaluation can be achieved by
understanding the polymerization fundamentals through mole
concept with least variations. The present research work focus
on the monomer mole ratio equivalency concept, for
understanding the theoretical preview of polymerization by
using chain extenders(CE) PEG-600(polyethylene glycol) ,
cross linkagers , (CLA):homogenous mixture of 1,4-
butanediol(BD) and 1,1,1-trimethylol propane (TMP) , curing
agents(CRA) 2,4-toluene diisocyanates .
Number of moles for each monomer unit is based on the
general formula [w/M]fN0 wherein w=wt.(g) , M(mol.wt),
f=functionality, N0 =Avagadro number, for ideal case of
polymerization, number of moles for all the monomer units
having OH functionalities should be equal to the number of
moles of curing agent with NCO functionality i.e [(w/M)fN0
]OH = [(w/M)fN0 ]NCO which is the IR( index ratio) 1 in ideal
case, based on this fundamental, models were proposed like
2nCE X 10 21 , 13nBD X 10 21, 13nTP X 10 21, for determining
the number of OH functionalities, for CE, BD, TMP
respectively n is weight in grams, while for number of NCO
functionalities of CRA( TDI) , by [7nTD-0.1] X 10 21, the
models for this PU system is time effective , for evaluating the
weight of CRA needed for linking all the OH functionalities
by carbamate links, a model[13,14] nTDI = [2nCE + 13nCLA
+0.1] / 7 is proposed with least variability , the research work
also envisages on the extent of polymerization independency
for the ratio of components of CLA but is the function of the
weight of CLA taken in the mixture, evaluated by the
proposed model ∑ OH𝑇𝑀𝑃n + ∑ OH𝐵𝐷
n = [W] CLAmix X 13
X 10 21 , total OH functionalities given by CLA & CE by
proposed model is given through[ 2nCE+13nCLA +0.1]
For IR values less than unity incomplete polymerization,
while for IR values unity effective/complete polymerization
was noticed.
EXPERIMENTAL
Materials
PEG-600 as CE (sigma aldrisch), TDI (2, 4 isomer, Sigma
Aldrisch) as CRA and homogenous mixture of BD (AR grade
Sigma Aldrisch) and TMP (AR grade Sigma Aldrisch) was
used as CLA .in order to remove any water content from
iisocyanate drying process was carried at 1050C to avoid
reaction between isocyantes and water forming CO2 bubbles,
which may deform the PU system. For casting wooden mold
was used, pre treated with silicon spray as mold release
(ALFA-40, JIVIKA company New Delhi). The cured PUC
was prepared as per the ASTMD638 Type I standards (Fig.1)
for evaluating mechanical properties by Universal Test
Machine UTE-40(FiE make, NEI limited, Gujrat. The Filler
used was fly ash( FA) for making FA-reinforced PUC, for
which FA was dried a at 110 ºC for 2.5 hours to remove any
moisture content which may further react with isocyanates
forming CO2 bubble which degrade PUC properties.
Fig1. FA-reinforced PU composite sample as per ASTM
D638 type I standard
Spectroscopic characterization of, CLA, CRA, PU-foam.
1,1,1-trimethylol propane (Fig.2) shows two bands of methyl
along with methylene around 2925cm-1 , 1,4-butanediol
(Fig.3) shows two peaks (symmetric and asymmetric
stretching bands ) of methylene only around 2925cm-1, The
binary component TMP &BD of CLA both shows a common
characterizing peak for OH group around 3200-3600cm-1
(Fig.4)
Fig2. IR spectra of TMP
Fig.3 IR spectra of BD
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12 (2019) pp. 2861-2872
© Research India Publications. http://www.ripublication.com
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Fig4. IR spectra of mixture of BD &TMP
Fig.5 IR spectra of TDI
CRA (Fig.5) characterized by band around 2249cm1
of –N=C=O functional group and aromatic ring characteristic
bands around 1522cm-1, 1578cm-1, and 1611cm-1.The CE,
PEG-600 (Fig.6), shows broad and less intense peak around
3200- 3600cm-1 indicating the presence of hydroxyl group,
while strong and intense peak around 2925cm-1 signifies the
presence of methylene group as a part of polymeric system.
The PUC formed is characterized by the formation of urethane
links –NHCOO- , shown by by the IR peaks of C=O around
1711 cm-1 and around 3309cm-1 for N-H stretching (Fig 7).
Fig.6 IR spectra of PEG-600
Fig.7 IR spectra PU-Composite
RESULTS AND DISCUSSION
Proposed models for CE, CLA and CRA.
The number of OH functionalities given by CE, CLA, and
NCO functionalities by CRA, IR and weight of curing agents
has been evaluated by the model proposed.
Monomers Proposed Models
PEG-600 ,f=2 Ʃ OH =2nCE X 10 21
TDI, f=2 Ʃ NCO =[7nTD-0.1] X 10 21
BD, f=2 Ʃ OH =13nBD X 10 21
TMP, f=3 Ʃ OH =13nTP X 10 21
IR(Index ratio) NCO/OH = [7nTD -0.1]/2nCE+13 nCLA
Wt. of Curing
Agents
Wt = [2nCE+13 nCLA +0.1] /7 g
Ʃ OH [CLA&CE] = 2nCE+13nCLA+0.1
.* n=wt in gm , f=functionality
The present research work focuses on the preparation of PU
matrix at constant weight ratio 3:2 of CE and CRA, while the
binary components (BD&TMP) of CLA were in 1:1, 1:2
&2:1weight ratios. Weight of CLA taken was either 0.5 or 1g
for the various weight ratios of binary components of CLA.
Using the proposed models Ʃ OH =2nCE X 10 21 for
evaluating the number of OH functionalities of CE(3g)it is
6X1021 and number of NCO functionalities by proposed
model Ʃ NCO =[7nTD-0.1] X 10 21 of CRA(2g) is 13.9 X 1021
were kept constant. In all the experiments wherein the sum
total of OH functionalities of CE and CLA(with all the weight
ratios of binary components & wt of CLA as either 0.5 or 1 g)
were equal to number of NCO[28] functionalities i.e 13.9 X
1021 complete polymerization was noticed. The values
evaluated by the proposed models for evaluating number of
OH &NCO functionalities, and Index ratio all were in good
agreement with those evaluated by mole concept[w/M]fN0
with least variability. The experiments are explained in the
tabulated form through proposed models.
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12 (2019) pp. 2861-2872
© Research India Publications. http://www.ripublication.com
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Evaluation of extent of complete Polymerization in PUC
by proposed model
[NCO/OH] IR=[7nTD-0.1]/2nCE+13 nCLA
The extent of polymerization evaluated by the IR of the PU
system calculated through proposed models were explained by
the SEM image showing the FA distribution in PUC. In the
experiments 1,3 &5 wherein 0.5 g of CLA was taken at all
wt/wt ratio of BD and TMP (1:1,1:2 and 2:1) the Ʃ NCO
functionalities ≥ Ʃ OH [CLA&CE] functionalities i.e [7nTD-
0.1] 10 21 ≥ [2nCE+13nCLA+0.1] 10 21 for various ratios of
BD and TMP of CLA. Complete polymerization with IR 1.1
evaluated by the proposed model for IR NCO/OH = [7nTD -
0.1]/2nCE+13 nCLA was supported by the SEM
images(Fig8,Fig10, and Fig12) wherein uniform distribution
of FA was seen in PU matrix.
Experiment 1 n = wt in gm
BD:TMP(ratio) 1:1
CLA (wt) 0.5g
Ʃ OH=13nBD X 10 21 3.25X1021
n=0.25
Ʃ OH=13nTP X 10 21 3.25X1021
n=0.25
Ʃ OH =2nCE X 10 21 6X1021
n=3
Ʃ OH(CLA& CE) 13.9X1021
n=2
Ʃ NCO=[7nTD-0.1] X 10 21 13.9X1021
n=2
NCO/OH=[7nTD-0.1]/2nCE+13 nCLA 1.1
[7nTD-0.1]≥2nCE+13nCLA+0.1 Complete
polymerization Fig.8. SEM image showing the formation of the FA reinforced
PUC (uniform distribution of FA in PU matrix)
Evaluation of extent of incomplete Polymerization by
proposed model.
[NCO/OH] IR=[7nTD-0.1]/2nCE+13 nCLA
The extent of polymerization was evaluated by the IR for the
PU system which was calculated through proposed models
and was explained by the SEM image showing FA
agglomeration over the small domain in PUC in the
experiments 2,4 &6 wherein 1 g of CLA was taken at all
wt/wt ratio of BD and TMP (1:1,1:2 and 2:1) the OH
[CLA&CE] functionalities ≥ Ʃ NCO functionalities i.e
[2nCE+13nCLA+0.1] 10 21 ≥ [7nTD-0.1] 10 21 for various ratios
of BD and TMP of CLA. Incomplete polymerization with IR
0.7 evaluated by the proposed model for IR NCO/OH = [7nTD
-0.1]/2nCE+13 nCLA was supported by the SEM
images(Fig9,Fig11, and Fig13) wherein non uniform
distribution/clumping of FA was seen in PU matrix.
Experiment 2 n = wt in gm
BD:TMP(ratio) 1:1
CLA (wt) 1g
Ʃ OH=13nBD X 10 21 6.5X1021
n=0.5
Ʃ OH=13nTP X 10 21 6.5 X1021
n=0.5
Ʃ OH =2nCE X 10 21 6X1021
n=3
Ʃ OH(CLA& CE) 19 X1021
Ʃ NCO=[7nTD-0.1] X 10 21 13.9X1021
n=2
NCO/OH=[7nTD-0.1]/2nCE+13 nCLA 0.7
2nCE+13nCLA+0.1≥[7nTD- 0.1] Incomplete
polymerization
Fig.9 SEM image showing the incomplete formation of the
FA reinforced PUC(FA clumping in PU matrix)
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12 (2019) pp. 2861-2872
© Research India Publications. http://www.ripublication.com
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Experiment 3 n = wt in gm
BD:TMP(ratio) 1:2
CLA (wt) 0.5g
Ʃ OH=13nBD X 10 21 2.0X1021
n=0.16
Ʃ OH=13nTP X 10 21 4.2X1021
n=0.33
Ʃ OH =2nCE X 10 21 6X1021
n=3
Ʃ OH(CLA& CE) 12.2X1021
Ʃ NCO=[7nTD-0.1] X 10 21 13.9X1021
n=2
NCO/OH=[7nTD-0.1]/2nCE+13 nCLA 1.1
[7nT- -0.1] ≥2nCE+13nCLA+0.1
Complete
polymerization
Fig.10. SEM image Showing the formation of the FA
reinforced PUC.(uniform distribution of FA in PU matrix
Experiment 4 n = wt in gm
BD:TMP(ratio) 1:2
CLA (wt) 1g
Ʃ OH=13nBD X 10 21 4.2X1021
n=0.33
Ʃ OH=13nTP X 10 21 8.5X1021
n=0.66
Ʃ OH =2nCE X 10 21 6X1021
n=3
Ʃ OH(CLA& CE) 18.7X1021
Ʃ NCO=[7nTD-0.1] X 10 21 13.9X1021
n=2
NCO/OH=[7nTD-0.1]/2nCE+13 nCLA 0.7
2nCE+13nCLA+0.1≥[7nTD- 0.1]
Incomplete
polymerization
Fig.11 SEM image showing the incomplete formation of the FA
reinforced PUC.(FA clustering in PU matrix)
Experiment 5 n = wt in gm
BD:TMP(ratio) 2:1
CLA (wt) 0.5g
Ʃ OH=13nBD X 10 21 4.2X1021
n=0.33
Ʃ OH=13nTP X 10 21 2.0X1021
n=0.16
Ʃ OH =2nCE X 10 21 6X1021
n=3
Ʃ OH(CLA& CE) 12.2X1021
Ʃ NCO=[7nTD-0.1] X 10 21 13.9X1021
n=2
NCO/OH=[7nTD-0.1]/2nCE+13 nCLA 1.1
[7nTD- 0.1] ≥2nCE+13nCLA+0.1
Complete
polymerization
Fig.12 SEM image Showing the formation of the FA reinforced
PUC (uniform distribution of FA in PU matrix)
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12 (2019) pp. 2861-2872
© Research India Publications. http://www.ripublication.com
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Experiment 6 n = wt in gm
BD:TMP(ratio) 2:1
CLA (wt) 1g
Ʃ OH=13nBD X 10 21 8.5X1021
n=0.66
Ʃ OH=13nTP X 10 21 4.2X1021
n=0.33
Ʃ OH =2nCE X 10 21 6X1021
n=3
Ʃ OH(CLA& CE) 18.7X1021
Ʃ NCO=[7nTD-0.1] X 10 21 13.9X1021
n=2
NCO/OH=[7nTD-0.1]/2nCE+13 nCLA 0.7
2nCE+13nCLA+0.1≥[7nTD- 0.1]
Incomplete
polymerization
Fig.13. SEM image showing the incomplete formation of the
FA reinforced PUC.(agglomeration of FA in PU matrix)
Graphical representation for model validation
Evaluating IR, number of OH functionalities of CE, BD, TMP and number of NCO functionalities of CRA simultaneously by
models and mole concept and validations of the values by both the methods is shown in 3D Fig 14,15,16,17,18,19,20 and 21.
Fig.14 comparison of number of OH functionalities of BD in CLA (1gm) by mole concept and by model
0
5
10
15
20
BD:TMP::1:1
BD:TMP::1:2
BD:TMP::2:1
6.6
4.38.6
0
6.5
4.2
8.5
0
model mole concept
Ratios of BD abd TMP in 1 gm of CLA
No
: o
f O
H
Fu
nct
ion
ali
ties
(10
21
)
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12 (2019) pp. 2861-2872
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Fig.15 comparison of number of OH functionalities of BD in CLA (0.5gm) by mole concept and by model
Fig.16 comparison of number of OH functionalities of TMP in CLA (1gm) by mole concept and by model
0
2
4
6
8
10
BD:TMP::1:1
BD:TMP::1:2
BD:TMP::2:1
3.22.1
4.3
3.2
24.2
Model moleconcept
Ratios of BD&TMP in 0.5gm of CLA
No
: o
f O
H
fun
ctio
na
liti
es(1
021
)
0
5
10
15
20
BD:TMP::1:1
BD:TMP::1:2
BD:TMP::2:1
6.58.5
4.2
model mole concept
No
:of
OH
fun
ctio
na
liti
es(1
021)
Ratios of BD and TMP in 1 gm of CLA
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12 (2019) pp. 2861-2872
© Research India Publications. http://www.ripublication.com
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Fig.17 comparison of number of OH functionalities of TMP in CLA (0.5gm) by mole concept and by model
Fig.18 Number of OH (1021) functionalities of CE by mole concept and by model
0
1
2
3
4
5
6
7
8
9
BD:TMP::1:1
BD:TMP::1:2
BD:TMP::2:1
3.34.3
2.1
3.2
4.2
2
model mole concept
Ratios of BD &TMP in 0.5 gm of CLA
No
: o
f O
H
fun
ctio
na
liti
es(1
021)
0
2
4
6
CE(gm)functionality
OH number by
mole concept OH number by
model
3
2
6 6
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Fig.19 Number of NCO (1021) functionalities of TDI by mole concept and by model
Fig.20. Comparison of Index Ratio (NCO/OH) for PUC when 0.5 gm of CLA taken at constant wt/wt ratio
of CE&CRA3:2 by model & mole concept.
Fig.21. Comparison of Index Ratio (NCO/OH) for PUC when 1 gm of CLA taken at constant wt/wt ratio
of CE&CRA3:2 by model & mole concept.
0
5
10
15
CRA(gm)functionality
NCOnumber by
mole concept NCOnumber by
model
22
13.8 13.9
mole concept
model0
2
BD:TMP::1:1BD:TMP::1:2
BD:TMP::2:1
1.11.1
1.1
1.1 1.11.1
mole conceptmodel
IND
EX
RA
TIO
N
CO
/OH
Ratios of BD & TMP in 0.5gm of CLA
mole concept
model0
0.2
0.4
0.6
0.8
BD:TMP:1:1BD:TMP:1:2
BD:TMP:2:1
0.70.7
0.7
0.7 0.7 0.7
mole concept model
Ratio of BD:TMP in 1 gm of CLA
IND
EX
RA
TIO
NC
O/O
H
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12 (2019) pp. 2861-2872
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Extent of polymerization is not the function of ratio of
binary components of CLA
In experiments for IR values 0.7 incomplete polymerization
was seen while for IR value as 1.1, complete polymerization
was noticed. PU synthesis having OH contribution from CE ,
CLA and NCO contribution from CRA evaluated by proposed
models were in good agreement with the mole concept
method. IR values evaluated by the mole concept and the
models were in great approximation. The present research
work also envisages on the independency of the ratio of
components of CLA on the extent of polymerization but
solely shows dependency on the weight of CLA taken in the
mixture: ∑ OH𝑇𝑀𝑃n + ∑ OH𝐵𝐷
n = [W] mix X 13 X 10 21 ,
general form for any ratio of BD and TMP when taken as
homogenous mixture
∑ OH𝑇𝑀𝑃n + ∑ OH𝐵𝐷
n = [(B/B+T) + ( T/B+T)] W X 13 X 10 21
∑ OH𝑇𝑀𝑃n + ∑ OH𝐵𝐷
n = [W] mix X 13 X 10 21
B=BD and T=TMP
Determination of mechanical properties of PUC
Mechanical properties viz. Tensile strength (TS), Young
modulus (YM) and hardness were evaluated for FA
reinforced PUC and were found to depend on the wt/wt ratio
of binary components of CLA which is shown by the UTM
graphes plotted between load v/s displacement(Fig.22,23,24).
Graphical representation of TS, YM and Hardness of FA
reinforced polyurethane composites with various ratios of BD
and TMP in CLA as 1:1(A), B (1:2) and C (2:1) is shown in
Fig.25.
Fig.22. load v/s displacement for PUC
at 1:1 w/w ratio of BD& TMP
Fig23. load v/s displacement for PUC
at 1:2 w/w ratio of BD&TMP
Fig.24. load v/s displacement for PUC
at 2:1 w/w ratio of BD& TMP
Fig.25. Graph representing TS, YM and Hardness of FA
reinforced polyurethane composites with various ratios
of BD and TMP in CLA as 1:1(A), B (1:2) and C (2:1).
CONCLUSION
For PU synthesis using BD and TMP homogenous mixture as
CLA, the extent of polymerization is independent of the ratio
of components of the CLA but depends on the amount of CLA
added to CE, however the mechanical property of polymer
[19,20,22] depends on the weight ratio of binary components
of CLA. The OH and NCO value calculated by using the mole
concept is in match with the one evaluated by using the
proposed models. The IR values evaluated for deciding the
extent of polymerization were in great agreement with values
through mole concept and by the proposed models. The
models proposed for this PU system is time effective and a
good mathematical tool for predicting the extent of
polymerization. When 0.5 g of CLA was added to 3g of CE,
the requisite amount of CRA for polymerization by the
proposed model Wt = [2nCE+13 nCLA +0.1] /7 g was 1.8g, for
which in experiment 2g was added which gave IR 1.1,
however for 1g of CLA with the same weight ratio of CE (3g)
requisite amount of CRA by the proposed model was 2.7g for
which only 2g was added in experiment giving IR only 0.7
3328
1316.5 14 6.5
52
76
38
0
10
20
30
40
50
60
70
80
A(1:1) B(1:2) C(2:1)
TS
YM
HRD
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12 (2019) pp. 2861-2872
© Research India Publications. http://www.ripublication.com
2871
Acknowledgements:
Authors wish to thank the Head, Department of Pure &
Applied Chemistry, University of Kota, Kota for providing
the necessary facilities.
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